Frobenius numbers associated with Diophantine triples of x²+y²=zʳ (extended version)

We give an explicit formula for the p-Frobenius number of triples associated with Diophantine equations x²+y²=zʳ, that is, the largest positive integer that can only be represented in p ways by combining the three integers of the solutions of Diophantine equations x²+y²=zʳ. When $r=2$, the Frobenius number has already been given.